The present invention relates generally to three-dimensional (3D) computerized tomography (CT) and, more particularly, the present invention relates to a method and system for processing cone beam projection data for reconstructing substantially free of boundary-induced artifacts a 3D image of a portion of an object.
Commonly assigned U.S. patent application Ser. No. 07/725,142 by Kwok C. Tam discloses method and apparatus for imaging a portion of an object irradiated in a field of view of a cone beam source such as a cone beam x-ray source or other suitable point source of radiant or electromagnetic energy. A portion of interest undergoing imaging inspection may be a preselected portion of an object which is wholly engulfed within the field of view of the cone beam source. Alternatively, the portion of interest to be imaged may be limited to only that portion of the object which fits within the field of view of the cone beam source, as is typically the case when the entire object is too large to be wholly irradiated thereby. In either case, the portion of interest can be rotationally scanned by the x-ray cone beam source at respective upper and lower extents thereof along a scan trajectory having upper and lower scan paths which serve to bound the portion of interest. To ensure that a complete Radon data set is acquired for exact image reconstruction, the upper and lower scan paths are connected by a connecting scan path to effectively provide a complete scan trajectory. Cone beam projection data is detected by a suitable surface array radiation detector wherein the source and array detector are mutually fixed with respect to one another so as to scan the portion of interest to acquire cone beam projection data for a plurality of source positions along the scan trajectory.
To insure exact image reconstruction, cone beam projection data is generally acquired using a technique which fills Radon space over a region of support in Radon space corresponding to the field of view occupied by the portion of interest of the object in real space. Such filling technique is chosen to provide sufficient Radon data to completely and exactly reconstruct a 3D CT image by a process of inverse Radon transformation. Preferably, at least a requisite core number of necessary data points in Radon space can be selectively retained for subsequent processing so as to exactly image the portion of interest. A 3D CT cone beam reconstructed image obtained by inverse Radon transformation utilizes a mathematical point by point inversion technique. The Radon inversion technique is inherently a computationally intensive technique which becomes unduly burdened by tracking Radon data points which either do not contribute or redundantly contribute to reconstruction of a 3D image of the portion of interest. Typically, either each Radon data point collected throughout Radon space is indiscriminately retained for point by point inversion processing, or a truncated subset of Radon data points, representing only cone beams which actually pass through the object, is selectively retained for point by point inversion processing. Truncation boundaries in Radon space are typically identified by the use of a projection and/or intersection operations which are easier to apply than direct point by point mathematical manipulations.
In a typical 3D CT reconstruction by Radon inversion, suitable integrals such as planar integrals are calculated and organized as discrete data points in Radon space. The planar integrals are based upon cone beam projection data measured by the detector. Radon data points are organized onto an arbitrary set of planes in Radon space, wherein each plane of integration is used to calculate a Radon derivative corresponding to a single data point in Radon space. These discretely organized Radon data points are typically partitioned and selectively retained or discarded according to whether or not corresponding planes of integration intersect the portion of interest of the object. By its mathematical nature, Radon space is a collection of discrete Radon data points each corresponding to a plane of integration, e.g., a planar integral. For each integration plane that intersects the portion of interest, the corresponding computation of a Radon derivative, i.e., a Radon data point, depends upon the manner in which that plane intersects with the portion of interest. Thus, the adequacy of filling the region of support in Radon space is generally assessed by first suitably partitioning those integration planes which contribute to data points in Radon space.
Typical image reconstruction of the portion of interest generally requires the following procedure: 1) identifying a plurality of suitable integration planes; 2) determining an appropriate angular range of the x-ray cone beam for each contributing source position required to compute the Radon derivative for each identified integration plane; and 3) keeping track of the exact number of source positions that contribute to a particular Radon data point. Commonly assigned U.S. patent application Ser. No. 07/908,114 by Kwok C. Tam improves the general approach of U.S. patent application Ser. No. 07/725,142 by pre-processing cone beam projection data for image reconstruction in a manner whereby only cone beam projection data acquired within a select region identified on the surface array detector is retained for further processing. Thus, image processing using the foregoing pre-processing conveniently requires fewer operations resulting in saving time, money and computer resources.
The approach of patent application Ser. No. 07/908,114 is illustrated in FIGS. 1a and 1b. FIG. 1a illustrates an object 22 wherein a cylindrical portion 23, for example, is the portion of interest undergoing inspection. This portion is labelled "X" and is bounded by an upper scan path 24, labelled "C.sub.1 ", and a lower scan path 26, labelled "C.sub.2 ", with a predetermined connecting scan path therebetween (not shown). For the sake of illustration and not of limitation, upper and lower scan paths 24 and 26, are herein illustrated as circular paths enclosing the cylindrical portion of interest 23. By way of example, consider cone beam source 28 along upper scan path 24 at source position A, a projection of upper and lower scan paths 24 and 26 from source position A onto surface array detector 32 can be characterized by a boundary projection operator "P" operating on scan paths 24 and 26, respectively. The boundary projection operation on the upper scan path can be symbolically represented by P(C.sub.1) and such upper scan path simply projects onto surface array detector 32 as a straight line 34. Similarly, boundary projection operation P(C.sub.2) can be shown to project the lower scan path onto detector 32 as a parabolic curve 36.
As illustrated in FIGS. 1a and 1b, a closed region 44 on surface array detector 32 results upon operation of a mask projection operator M conceptually represented by a suitably identified region 38 in the square designated as M. Mask projection operator M upon operating on an overall cone beam projection 42 of the object 22 and cooperating with boundary operator P advantageously provides closed region 44 further shown in the square designated as MP(X). Thus, closed region 44 is obtained by taking the intersection of the overall cone beam projection 42 of object 22 with mask operator M (i.e., region 38) onto surface detector 32 wherein such intersection is bounded by P(C.sub.1) at straight line 34 and P(C.sub.2) at parabolic curve 36. Thus cone beam projection data can be acquired at the array detector for each position along the scan trajectory, retaining only that cone beam projection data acquired within region 38 for further processing. This manner of pre-processing data amounts to processing only data collected within region 38 which matches the cone beam projection of the object bounded between the respective similar projections of the upper and lower scan paths. Region 38 is herein referred to as a masked cone beam region.
For the sake of explanation, a given exemplary energy cone beam detected at surface array detector 32 within region 38, can represent, for example, the cone beam emitted from source scan position A, within an angle conveniently chosen to span at least the boundaries or edges defined by projection of upper scan path C.sub.1, at straight line 34, and the projection of lower scan path C.sub.2, at parabolic curve 36. Thus, it will be appreciated that such exemplary cone beam intersects at least certain predetermined subportion of portion of interest 23 being that the upper and lower scan paths as well as the connecting path cooperate to fully enclose portion of interest 23. Additional source scan positions can provide cone beam projections which are limited to within the masked cone beam region. In essence, such cone beam projections are obtained from cone beams which can be characterized as passing only through portion of interest 23 (labelled as X) without contamination by the rest of object 22, i.e., remaining portions of the object other than portion X. Based upon the above characterization there is no longer a need to distinguish between different categories of integration planes by partitioning those integration planes which contribute to data points in Radon space. Although such otherwise requisite partitioning procedure is therefore eliminated which results in saving time, money and computer resources, certain image artifacts unfortunately can occur.
To obtain cone beam projection data uncontaminated by the rest of object 22, it will be appreciated that cone beam projection data acquired outside region 38 is set to a zero value, i.e., individual detector elements such as pixel detectors situated outside the masked cone beam region are collectively set to have a respective value of zero. In particular, whenever a line of integration intersects the boundary defined by parabolic curve 36 (i.e., the lower scan path projection) boundary-induced artifacts can occur. For instance, such boundary-induced artifacts typically arise because the line of integration may loose contribution of cone beam projection data from points situated outside region 38 and in particular outside parabolic curve 36. For instance lines of integration used in calculating Radon data for the portion of interest may no longer exhibit a suitable mapping relationship for points situated along such boundary intersecting lines of integration, and generally result in an image having noticeable boundary-induced artifacts. (No representation is made or intended that these referenced applications are necessarily prior art to the present application).